Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [980,2,Mod(569,980)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(980, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("980.569");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 980 = 2^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 980.q (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82533939809\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 569.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 980.569 |
Dual form | 980.2.q.c.949.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/980\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(197\) | \(491\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.59808 | − | 1.50000i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.86603 | + | 1.23205i | −0.834512 | + | 0.550990i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000 | − | 5.19615i | 1.00000 | − | 1.73205i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.50000 | − | 2.59808i | −0.452267 | − | 0.783349i | 0.546259 | − | 0.837616i | \(-0.316051\pi\) |
−0.998526 | + | 0.0542666i | \(0.982718\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | 0.990338 | + | 0.138675i | \(0.0442844\pi\) | ||||
−0.990338 | + | 0.138675i | \(0.955716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00000 | + | 6.00000i | −0.774597 | + | 1.54919i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.33013 | − | 2.50000i | 1.05021 | − | 0.606339i | 0.127502 | − | 0.991838i | \(-0.459304\pi\) |
0.922708 | + | 0.385499i | \(0.125971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 6.92820i | 0.917663 | − | 1.58944i | 0.114708 | − | 0.993399i | \(-0.463407\pi\) |
0.802955 | − | 0.596040i | \(-0.203260\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.73205 | + | 1.00000i | 0.361158 | + | 0.208514i | 0.669588 | − | 0.742732i | \(-0.266471\pi\) |
−0.308431 | + | 0.951247i | \(0.599804\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.96410 | − | 4.59808i | 0.392820 | − | 0.919615i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 9.00000i | − | 1.73205i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | 0.0928477 | − | 0.995680i | \(-0.470403\pi\) | ||||
0.0928477 | + | 0.995680i | \(0.470403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | − | 1.73205i | −0.179605 | − | 0.311086i | 0.762140 | − | 0.647412i | \(-0.224149\pi\) |
−0.941745 | + | 0.336327i | \(0.890815\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.79423 | − | 4.50000i | −1.35680 | − | 0.783349i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.66025 | − | 5.00000i | −1.42374 | − | 0.821995i | −0.427121 | − | 0.904194i | \(-0.640472\pi\) |
−0.996616 | + | 0.0821995i | \(0.973806\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.50000 | + | 2.59808i | 0.240192 | + | 0.416025i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000 | 0.937043 | 0.468521 | − | 0.883452i | \(-0.344787\pi\) | ||||
0.468521 | + | 0.883452i | \(0.344787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.803848 | + | 13.3923i | 0.119831 | + | 1.99641i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.52628 | + | 5.50000i | 1.38955 | + | 0.802257i | 0.993264 | − | 0.115870i | \(-0.0369655\pi\) |
0.396286 | + | 0.918127i | \(0.370299\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.50000 | − | 12.9904i | 1.05021 | − | 1.81902i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.19615 | + | 3.00000i | −0.713746 | + | 0.412082i | −0.812447 | − | 0.583036i | \(-0.801865\pi\) |
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.00000 | + | 3.00000i | 0.809040 | + | 0.404520i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 24.0000i | − | 3.17888i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.00000 | + | 8.66025i | 0.650945 | + | 1.12747i | 0.982894 | + | 0.184172i | \(0.0589603\pi\) |
−0.331949 | + | 0.943297i | \(0.607706\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.23205 | − | 1.86603i | −0.152817 | − | 0.231452i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.66025 | + | 5.00000i | −1.05802 | + | 0.610847i | −0.924883 | − | 0.380251i | \(-0.875838\pi\) |
−0.133135 | + | 0.991098i | \(0.542504\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.00000 | 0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −8.66025 | + | 5.00000i | −1.01361 | + | 0.585206i | −0.912245 | − | 0.409644i | \(-0.865653\pi\) |
−0.101361 | + | 0.994850i | \(0.532320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.79423 | − | 14.8923i | −0.207180 | − | 1.71962i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50000 | + | 6.06218i | −0.393781 | + | 0.682048i | −0.992945 | − | 0.118578i | \(-0.962166\pi\) |
0.599164 | + | 0.800626i | \(0.295500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00000 | + | 10.0000i | −0.542326 | + | 1.08465i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.59808 | − | 1.50000i | 0.278543 | − | 0.160817i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.00000 | + | 6.92820i | −0.423999 | + | 0.734388i | −0.996326 | − | 0.0856373i | \(-0.972707\pi\) |
0.572327 | + | 0.820025i | \(0.306041\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.19615 | − | 3.00000i | −0.538816 | − | 0.311086i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.07180 | + | 17.8564i | 0.109964 | + | 1.83203i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.00000i | − | 0.304604i | −0.988334 | − | 0.152302i | \(-0.951331\pi\) | ||
0.988334 | − | 0.152302i | \(-0.0486686\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18.0000 | −1.80907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.00000 | − | 10.3923i | −0.597022 | − | 1.03407i | −0.993258 | − | 0.115924i | \(-0.963017\pi\) |
0.396236 | − | 0.918149i | \(-0.370316\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.33013 | + | 2.50000i | 0.426660 | + | 0.246332i | 0.697923 | − | 0.716173i | \(-0.254108\pi\) |
−0.271263 | + | 0.962505i | \(0.587441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.92820 | − | 4.00000i | −0.669775 | − | 0.386695i | 0.126217 | − | 0.992003i | \(-0.459717\pi\) |
−0.795991 | + | 0.605308i | \(0.793050\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.50000 | − | 6.06218i | −0.335239 | − | 0.580651i | 0.648292 | − | 0.761392i | \(-0.275484\pi\) |
−0.983531 | + | 0.180741i | \(0.942150\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −30.0000 | −2.84747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.0000i | 0.940721i | 0.882474 | + | 0.470360i | \(0.155876\pi\) | ||||
−0.882474 | + | 0.470360i | \(0.844124\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.46410 | + | 0.267949i | −0.416280 | + | 0.0249864i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.19615 | + | 3.00000i | 0.480384 | + | 0.277350i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | − | 1.73205i | 0.0909091 | − | 0.157459i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 15.5885 | − | 9.00000i | 1.40556 | − | 0.811503i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.00000 | + | 11.0000i | 0.178885 | + | 0.983870i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.00000 | + | 10.3923i | 0.528271 | + | 0.914991i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | − | 1.73205i | 0.0873704 | − | 0.151330i | −0.819028 | − | 0.573753i | \(-0.805487\pi\) |
0.906399 | + | 0.422423i | \(0.138820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 11.0885 | + | 16.7942i | 0.954342 | + | 1.44542i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.46410 | − | 2.00000i | 0.295958 | − | 0.170872i | −0.344668 | − | 0.938725i | \(-0.612008\pi\) |
0.640626 | + | 0.767853i | \(0.278675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.0000 | 0.848189 | 0.424094 | − | 0.905618i | \(-0.360592\pi\) | ||||
0.424094 | + | 0.905618i | \(0.360592\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 33.0000 | 2.77910 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.59808 | − | 1.50000i | 0.217262 | − | 0.125436i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.86603 | + | 1.23205i | −0.154965 | + | 0.102316i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.00000 | + | 5.19615i | −0.245770 | + | 0.425685i | −0.962348 | − | 0.271821i | \(-0.912374\pi\) |
0.716578 | + | 0.697507i | \(0.245707\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.50000 | − | 7.79423i | −0.366205 | − | 0.634285i | 0.622764 | − | 0.782410i | \(-0.286010\pi\) |
−0.988969 | + | 0.148124i | \(0.952676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 30.0000i | − | 2.42536i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.00000 | + | 2.00000i | 0.321288 | + | 0.160644i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.5885 | − | 9.00000i | 1.24409 | − | 0.718278i | 0.274169 | − | 0.961681i | \(-0.411597\pi\) |
0.969925 | + | 0.243403i | \(0.0782638\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −9.00000 | + | 15.5885i | −0.713746 | + | 1.23625i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.19615 | + | 3.00000i | 0.406994 | + | 0.234978i | 0.689497 | − | 0.724288i | \(-0.257831\pi\) |
−0.282503 | + | 0.959266i | \(0.591165\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.0885 | − | 1.20577i | 1.56388 | − | 0.0938692i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 3.00000i | − | 0.232147i | −0.993241 | − | 0.116073i | \(-0.962969\pi\) | ||
0.993241 | − | 0.116073i | \(-0.0370308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.0000 | 0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −24.0000 | − | 41.5692i | −1.83533 | − | 3.17888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.79423 | + | 4.50000i | 0.592584 | + | 0.342129i | 0.766119 | − | 0.642699i | \(-0.222185\pi\) |
−0.173534 | + | 0.984828i | \(0.555519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 25.9808 | + | 15.0000i | 1.95283 | + | 1.12747i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.00000 | + | 3.46410i | 0.149487 | + | 0.258919i | 0.931038 | − | 0.364922i | \(-0.118904\pi\) |
−0.781551 | + | 0.623841i | \(0.785571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0000 | 0.743294 | 0.371647 | − | 0.928374i | \(-0.378793\pi\) | ||||
0.371647 | + | 0.928374i | \(0.378793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 22.3205 | − | 1.33975i | 1.64104 | − | 0.0985001i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −12.9904 | − | 7.50000i | −0.949951 | − | 0.548454i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.50000 | + | 6.06218i | −0.253251 | + | 0.438644i | −0.964419 | − | 0.264378i | \(-0.914833\pi\) |
0.711168 | + | 0.703022i | \(0.248167\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.92820 | + | 4.00000i | −0.498703 | + | 0.287926i | −0.728178 | − | 0.685388i | \(-0.759632\pi\) |
0.229475 | + | 0.973315i | \(0.426299\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.00000 | − | 3.00000i | −0.429669 | − | 0.214834i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.0000i | 0.712470i | 0.934396 | + | 0.356235i | \(0.115940\pi\) | ||||
−0.934396 | + | 0.356235i | \(0.884060\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.00000 | − | 15.5885i | −0.637993 | − | 1.10504i | −0.985873 | − | 0.167497i | \(-0.946431\pi\) |
0.347879 | − | 0.937539i | \(-0.386902\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.0000 | + | 25.9808i | −1.05802 | + | 1.83254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.1962 | + | 7.39230i | −0.781973 | + | 0.516301i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3923 | − | 6.00000i | 0.722315 | − | 0.417029i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −24.0000 | −1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.00000 | −0.206529 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.92820 | − | 7.46410i | −0.336101 | − | 0.509048i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −15.0000 | + | 25.9808i | −1.01361 | + | 1.75562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.50000 | + | 4.33013i | 0.168168 | + | 0.291276i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.0000i | 1.27233i | 0.771551 | + | 0.636167i | \(0.219481\pi\) | ||||
−0.771551 | + | 0.636167i | \(0.780519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −18.0000 | − | 24.0000i | −1.20000 | − | 1.60000i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.3827 | + | 13.5000i | −1.55196 | + | 0.896026i | −0.553981 | + | 0.832529i | \(0.686892\pi\) |
−0.997982 | + | 0.0634974i | \(0.979775\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0000 | − | 22.5167i | 0.859064 | − | 1.48794i | −0.0137585 | − | 0.999905i | \(-0.504380\pi\) |
0.872823 | − | 0.488037i | \(-0.162287\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.8564 | + | 8.00000i | 0.907763 | + | 0.524097i | 0.879711 | − | 0.475509i | \(-0.157736\pi\) |
0.0280525 | + | 0.999606i | \(0.491069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5526 | + | 1.47372i | −1.60163 | + | 0.0961349i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 21.0000i | 1.36410i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.00000 | −0.323423 | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||||
−0.161712 | + | 0.986838i | \(0.551701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.00000 | − | 15.5885i | −0.579741 | − | 1.00414i | −0.995509 | − | 0.0946700i | \(-0.969820\pi\) |
0.415768 | − | 0.909471i | \(-0.363513\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.92820 | + | 4.00000i | 0.440831 | + | 0.254514i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 18.0000 | + | 31.1769i | 1.14070 | + | 1.97576i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.00000 | −0.126239 | −0.0631194 | − | 0.998006i | \(-0.520105\pi\) | ||||
−0.0631194 | + | 0.998006i | \(0.520105\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 6.00000i | − | 0.377217i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.00962 | + | 33.4808i | 0.125847 | + | 2.09665i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.19615 | + | 3.00000i | 0.324127 | + | 0.187135i | 0.653231 | − | 0.757159i | \(-0.273413\pi\) |
−0.329104 | + | 0.944294i | \(0.606747\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.00000 | − | 5.19615i | 0.185695 | − | 0.321634i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.7846 | − | 12.0000i | 1.28163 | − | 0.739952i | 0.304487 | − | 0.952517i | \(-0.401515\pi\) |
0.977147 | + | 0.212565i | \(0.0681817\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.00000 | − | 12.0000i | 0.368577 | − | 0.737154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.0000i | 1.46878i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.00000 | − | 1.73205i | −0.0609711 | − | 0.105605i | 0.833929 | − | 0.551872i | \(-0.186086\pi\) |
−0.894900 | + | 0.446267i | \(0.852753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.8923 | + | 1.79423i | −0.898040 | + | 0.108196i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.1244 | + | 7.00000i | −0.728482 | + | 0.420589i | −0.817867 | − | 0.575408i | \(-0.804843\pi\) |
0.0893846 | + | 0.995997i | \(0.471510\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.0000 | 0.894825 | 0.447412 | − | 0.894328i | \(-0.352346\pi\) | ||||
0.447412 | + | 0.894328i | \(0.352346\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.06218 | + | 3.50000i | −0.360359 | + | 0.208053i | −0.669238 | − | 0.743048i | \(-0.733379\pi\) |
0.308879 | + | 0.951101i | \(0.400046\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 29.5692 | + | 44.7846i | 1.75153 | + | 2.65281i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | − | 6.92820i | 0.235294 | − | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.50000 | − | 7.79423i | −0.263795 | − | 0.456906i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.0000i | 0.876309i | 0.898900 | + | 0.438155i | \(0.144368\pi\) | ||||
−0.898900 | + | 0.438155i | \(0.855632\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20.0000 | − | 10.0000i | −1.16445 | − | 0.582223i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.3827 | + | 13.5000i | −1.35680 | + | 0.783349i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.1769 | − | 18.0000i | −1.79107 | − | 1.03407i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0000i | 1.08439i | 0.840254 | + | 0.542194i | \(0.182406\pi\) | ||||
−0.840254 | + | 0.542194i | \(0.817594\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.00000 | + | 10.3923i | 0.340229 | + | 0.589294i | 0.984475 | − | 0.175525i | \(-0.0561621\pi\) |
−0.644246 | + | 0.764818i | \(0.722829\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.06218 | + | 3.50000i | 0.342655 | + | 0.197832i | 0.661445 | − | 0.749993i | \(-0.269943\pi\) |
−0.318791 | + | 0.947825i | \(0.603277\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −24.2487 | − | 14.0000i | −1.36194 | − | 0.786318i | −0.372061 | − | 0.928208i | \(-0.621349\pi\) |
−0.989882 | + | 0.141890i | \(0.954682\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.50000 | − | 2.59808i | −0.0839839 | − | 0.145464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −24.0000 | −1.33955 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 40.0000i | − | 2.22566i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.59808 | + | 1.96410i | 0.255055 | + | 0.108949i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1865 | − | 10.5000i | −1.00572 | − | 0.580651i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.0000 | + | 17.3205i | −0.549650 | + | 0.952021i | 0.448649 | + | 0.893708i | \(0.351905\pi\) |
−0.998298 | + | 0.0583130i | \(0.981428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −51.9615 | + | 30.0000i | −2.84747 | + | 1.64399i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.0000 | − | 20.0000i | 0.546358 | − | 1.09272i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000i | 1.19842i | 0.800593 | + | 0.599208i | \(0.204518\pi\) | ||||
−0.800593 | + | 0.599208i | \(0.795482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.0000 | + | 25.9808i | 0.814688 | + | 1.41108i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.00000 | + | 5.19615i | −0.162459 | + | 0.281387i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −11.1962 | + | 7.39230i | −0.602781 | + | 0.397988i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 15.5885 | − | 9.00000i | 0.836832 | − | 0.483145i | −0.0193540 | − | 0.999813i | \(-0.506161\pi\) |
0.856186 | + | 0.516667i | \(0.172828\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 36.0000 | 1.92704 | 0.963518 | − | 0.267644i | \(-0.0862451\pi\) | ||||
0.963518 | + | 0.267644i | \(0.0862451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.00000 | 0.480384 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.79423 | + | 4.50000i | −0.414845 | + | 0.239511i | −0.692869 | − | 0.721063i | \(-0.743654\pi\) |
0.278024 | + | 0.960574i | \(0.410320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 14.0000 | − | 24.2487i | 0.738892 | − | 1.27980i | −0.214103 | − | 0.976811i | \(-0.568683\pi\) |
0.952995 | − | 0.302987i | \(-0.0979839\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.5000 | − | 38.9711i | −1.18421 | − | 2.05111i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 6.00000i | − | 0.314918i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.0000 | − | 20.0000i | 0.523424 | − | 1.04685i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −16.4545 | + | 9.50000i | −0.858917 | + | 0.495896i | −0.863649 | − | 0.504093i | \(-0.831827\pi\) |
0.00473247 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 18.0000 | − | 31.1769i | 0.937043 | − | 1.62301i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.7128 | + | 16.0000i | 1.43492 | + | 0.828449i | 0.997490 | − | 0.0708063i | \(-0.0225572\pi\) |
0.437425 | + | 0.899255i | \(0.355891\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.6962 | + | 25.5788i | 1.12038 | + | 1.32089i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.00000i | 0.0515026i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.0000 | −1.43826 | −0.719132 | − | 0.694874i | \(-0.755460\pi\) | ||||
−0.719132 | + | 0.694874i | \(0.755460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.00000 | − | 5.19615i | −0.153695 | − | 0.266207i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.7846 | + | 12.0000i | 1.05654 | + | 0.609994i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.50000 | + | 7.79423i | 0.228159 | + | 0.395183i | 0.957263 | − | 0.289220i | \(-0.0933960\pi\) |
−0.729103 | + | 0.684403i | \(0.760063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.0000 | 0.505722 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 6.00000i | − | 0.302660i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.937822 | − | 15.6244i | −0.0471870 | − | 0.786147i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.7224 | − | 8.50000i | −0.738898 | − | 0.426603i | 0.0827707 | − | 0.996569i | \(-0.473623\pi\) |
−0.821668 | + | 0.569966i | \(0.806956\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.5000 | − | 23.3827i | 0.674158 | − | 1.16768i | −0.302556 | − | 0.953131i | \(-0.597840\pi\) |
0.976714 | − | 0.214544i | \(-0.0688266\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.73205 | − | 1.00000i | 0.0862796 | − | 0.0498135i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 18.0000 | + | 9.00000i | 0.894427 | + | 0.447214i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 30.0000i | 1.48704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.00000 | − | 3.46410i | −0.0988936 | − | 0.171289i | 0.812333 | − | 0.583193i | \(-0.198197\pi\) |
−0.911227 | + | 0.411905i | \(0.864864\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.00000 | − | 10.3923i | 0.295958 | − | 0.512615i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7846 | − | 22.3923i | −0.725748 | − | 1.09920i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 25.9808 | − | 15.0000i | 1.27228 | − | 0.734553i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.00000 | 0.0977064 | 0.0488532 | − | 0.998806i | \(-0.484443\pi\) | ||||
0.0488532 | + | 0.998806i | \(0.484443\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −23.0000 | −1.12095 | −0.560476 | − | 0.828171i | \(-0.689382\pi\) | ||||
−0.560476 | + | 0.828171i | \(0.689382\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 57.1577 | − | 33.0000i | 2.77910 | − | 1.60451i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.99038 | − | 24.8205i | −0.145055 | − | 1.20397i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 4.50000 | − | 7.79423i | 0.217262 | − | 0.376309i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.5000 | + | 32.0429i | 0.891114 | + | 1.54345i | 0.838542 | + | 0.544837i | \(0.183408\pi\) |
0.0525716 | + | 0.998617i | \(0.483258\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 38.0000i | − | 1.82616i | −0.407777 | − | 0.913082i | \(-0.633696\pi\) | ||
0.407777 | − | 0.913082i | \(-0.366304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.00000 | + | 6.00000i | −0.143839 | + | 0.287678i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 13.8564 | − | 8.00000i | 0.662842 | − | 0.382692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.0000 | + | 22.5167i | −0.620456 | + | 1.07466i | 0.368945 | + | 0.929451i | \(0.379719\pi\) |
−0.989401 | + | 0.145210i | \(0.953614\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.3923 | + | 6.00000i | 0.493753 | + | 0.285069i | 0.726130 | − | 0.687557i | \(-0.241317\pi\) |
−0.232377 | + | 0.972626i | \(0.574650\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.07180 | − | 17.8564i | −0.0508080 | − | 0.846475i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.0000i | 0.851371i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.0000 | −0.519122 | −0.259561 | − | 0.965727i | \(-0.583578\pi\) | ||||
−0.259561 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.00000 | − | 15.5885i | −0.423793 | − | 0.734032i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −23.3827 | − | 13.5000i | −1.09861 | − | 0.634285i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 19.0526 | + | 11.0000i | 0.891241 | + | 0.514558i | 0.874348 | − | 0.485299i | \(-0.161289\pi\) |
0.0168929 | + | 0.999857i | \(0.494623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −22.5000 | − | 38.9711i | −1.05021 | − | 1.81902i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 4.00000i | − | 0.185896i | −0.995671 | − | 0.0929479i | \(-0.970371\pi\) | ||
0.995671 | − | 0.0929479i | \(-0.0296290\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.3923 | − | 0.803848i | 0.621053 | − | 0.0372775i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.9186 | − | 11.5000i | −0.921722 | − | 0.532157i | −0.0375381 | − | 0.999295i | \(-0.511952\pi\) |
−0.884184 | + | 0.467139i | \(0.845285\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 27.0000 | − | 46.7654i | 1.24409 | − | 2.15483i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 10.3923 | − | 6.00000i | 0.477839 | − | 0.275880i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.0000 | − | 32.0000i | −1.10120 | − | 1.46826i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 36.0000i | 1.64833i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.00000 | + | 15.5885i | 0.411220 | + | 0.712255i | 0.995023 | − | 0.0996406i | \(-0.0317693\pi\) |
−0.583803 | + | 0.811895i | \(0.698436\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.00000 | − | 8.66025i | 0.227980 | − | 0.394874i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.69615 | + | 5.59808i | 0.167834 | + | 0.254196i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −22.5167 | + | 13.0000i | −1.02033 | + | 0.589086i | −0.914199 | − | 0.405266i | \(-0.867179\pi\) |
−0.106129 | + | 0.994352i | \(0.533846\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.0000 | 0.813988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0000 | 1.48927 | 0.744635 | − | 0.667472i | \(-0.232624\pi\) | ||||
0.744635 | + | 0.667472i | \(0.232624\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.33013 | − | 2.50000i | 0.195019 | − | 0.112594i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 33.5885 | − | 22.1769i | 1.50969 | − | 0.996778i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.5000 | + | 25.1147i | −0.649109 | + | 1.12429i | 0.334227 | + | 0.942493i | \(0.391525\pi\) |
−0.983336 | + | 0.181797i | \(0.941809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.50000 | − | 7.79423i | −0.201045 | − | 0.348220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.00000i | 0.0445878i | 0.999751 | + | 0.0222939i | \(0.00709696\pi\) | ||||
−0.999751 | + | 0.0222939i | \(0.992903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 24.0000 | + | 12.0000i | 1.06799 | + | 0.533993i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 31.1769 | − | 18.0000i | 1.38462 | − | 0.799408i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.0000 | + | 22.5167i | −0.576215 | + | 0.998033i | 0.419694 | + | 0.907666i | \(0.362138\pi\) |
−0.995908 | + | 0.0903676i | \(0.971196\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −62.3538 | − | 36.0000i | −2.75299 | − | 1.58944i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.1603 | + | 0.669873i | −0.491780 | + | 0.0295181i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.0000i | − | 1.45134i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 27.0000 | 1.18517 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | + | 10.3923i | 0.262865 | + | 0.455295i | 0.967002 | − | 0.254769i | \(-0.0819994\pi\) |
−0.704137 | + | 0.710064i | \(0.748666\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3205 | + | 10.0000i | 0.757373 | + | 0.437269i | 0.828352 | − | 0.560208i | \(-0.189279\pi\) |
−0.0709788 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.66025 | − | 5.00000i | −0.377247 | − | 0.217803i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.50000 | − | 16.4545i | −0.413043 | − | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 60.0000 | 2.60378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.00000i | 0.259889i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 17.8564 | − | 1.07180i | 0.772000 | − | 0.0463378i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.3923 | + | 6.00000i | 0.448461 | + | 0.258919i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.5000 | − | 21.6506i | 0.537417 | − | 0.930834i | −0.461625 | − | 0.887075i | \(-0.652733\pi\) |
0.999042 | − | 0.0437584i | \(-0.0139332\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.9808 | − | 15.0000i | 1.11494 | − | 0.643712i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | + | 7.00000i | 0.599694 | + | 0.299847i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 8.00000i | − | 0.342055i | −0.985266 | − | 0.171028i | \(-0.945291\pi\) | ||
0.985266 | − | 0.171028i | \(-0.0547087\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 55.9808 | − | 36.9615i | 2.37625 | − | 1.56893i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.3205 | − | 10.0000i | 0.733893 | − | 0.423714i | −0.0859514 | − | 0.996299i | \(-0.527393\pi\) |
0.819845 | + | 0.572586i | \(0.194060\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.00000 | −0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −45.0000 | −1.89990 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.8564 | + | 8.00000i | −0.583978 | + | 0.337160i | −0.762713 | − | 0.646737i | \(-0.776133\pi\) |
0.178735 | + | 0.983897i | \(0.442800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.3205 | − | 18.6603i | −0.518328 | − | 0.785043i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.00000 | − | 15.5885i | 0.377300 | − | 0.653502i | −0.613369 | − | 0.789797i | \(-0.710186\pi\) |
0.990668 | + | 0.136295i | \(0.0435194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.0000 | − | 17.3205i | −0.418487 | − | 0.724841i | 0.577301 | − | 0.816532i | \(-0.304106\pi\) |
−0.995788 | + | 0.0916910i | \(0.970773\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.0000i | 0.877288i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | − | 6.00000i | 0.333623 | − | 0.250217i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −14.7224 | + | 8.50000i | −0.612903 | + | 0.353860i | −0.774101 | − | 0.633062i | \(-0.781798\pi\) |
0.161198 | + | 0.986922i | \(0.448464\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.0000 | + | 20.7846i | −0.498703 | + | 0.863779i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 15.5885 | + | 9.00000i | 0.645608 | + | 0.372742i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3923 | + | 0.803848i | −0.553704 | + | 0.0332350i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 28.0000i | − | 1.15568i | −0.816149 | − | 0.577842i | \(-0.803895\pi\) | ||
0.816149 | − | 0.577842i | \(-0.196105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | −0.659269 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 15.0000 | + | 25.9808i | 0.617018 | + | 1.06871i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.59808 | + | 1.50000i | 0.106690 | + | 0.0615976i | 0.552396 | − | 0.833582i | \(-0.313714\pi\) |
−0.445705 | + | 0.895180i | \(0.647047\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −46.7654 | − | 27.0000i | −1.91398 | − | 1.10504i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.5000 | − | 18.1865i | −0.429018 | − | 0.743082i | 0.567768 | − | 0.823189i | \(-0.307807\pi\) |
−0.996786 | + | 0.0801071i | \(0.974474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 60.0000i | 2.44339i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.267949 | + | 4.46410i | 0.0108937 | + | 0.181492i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.33013 | + | 2.50000i | 0.175754 | + | 0.101472i | 0.585296 | − | 0.810819i | \(-0.300978\pi\) |
−0.409542 | + | 0.912291i | \(0.634311\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.50000 | + | 9.52628i | −0.222506 | + | 0.385392i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3923 | − | 6.00000i | 0.419741 | − | 0.242338i | −0.275225 | − | 0.961380i | \(-0.588752\pi\) |
0.694967 | + | 0.719042i | \(0.255419\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −18.0000 | + | 36.0000i | −0.725830 | + | 1.45166i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 34.0000i | − | 1.36879i | −0.729112 | − | 0.684394i | \(-0.760067\pi\) | ||
0.729112 | − | 0.684394i | \(-0.239933\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.00000 | + | 1.73205i | 0.0401934 | + | 0.0696170i | 0.885422 | − | 0.464787i | \(-0.153869\pi\) |
−0.845229 | + | 0.534404i | \(0.820536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.00000 | − | 15.5885i | 0.361158 | − | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.2846 | − | 18.0622i | −0.691384 | − | 0.722487i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −62.3538 | + | 36.0000i | −2.49017 | + | 1.43770i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −50.0000 | −1.99363 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.0000 | 0.597141 | 0.298570 | − | 0.954388i | \(-0.403490\pi\) | ||||
0.298570 | + | 0.954388i | \(0.403490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.79423 | + | 4.50000i | −0.309793 | + | 0.178859i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.46410 | + | 3.73205i | 0.0977849 | + | 0.148102i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.0000 | + | 22.5167i | 0.513469 | + | 0.889355i | 0.999878 | + | 0.0156233i | \(0.00497325\pi\) |
−0.486409 | + | 0.873731i | \(0.661693\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.00000i | − | 0.197181i | −0.995128 | − | 0.0985904i | \(-0.968567\pi\) | ||
0.995128 | − | 0.0985904i | \(-0.0314334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −24.0000 | − | 12.0000i | −0.944999 | − | 0.472500i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7846 | − | 12.0000i | 0.817127 | − | 0.471769i | −0.0322975 | − | 0.999478i | \(-0.510282\pi\) |
0.849425 | + | 0.527710i | \(0.176949\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.0000 | − | 25.9808i | 0.588802 | − | 1.01983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 31.1769 | + | 18.0000i | 1.22005 | + | 0.704394i | 0.964928 | − | 0.262515i | \(-0.0845520\pi\) |
0.255119 | + | 0.966910i | \(0.417885\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.267949 | + | 4.46410i | 0.0104696 | + | 0.174427i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 60.0000i | 2.34082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −39.0000 | −1.51922 | −0.759612 | − | 0.650376i | \(-0.774611\pi\) | ||||
−0.759612 | + | 0.650376i | \(0.774611\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.0000 | + | 24.2487i | 0.544537 | + | 0.943166i | 0.998636 | + | 0.0522143i | \(0.0166279\pi\) |
−0.454099 | + | 0.890951i | \(0.650039\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.9904 | + | 7.50000i | 0.504505 | + | 0.291276i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.73205 | + | 1.00000i | 0.0670653 | + | 0.0387202i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.5000 | + | 49.3634i | 1.10187 | + | 1.90850i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 16.0000i | 0.616755i | 0.951264 | + | 0.308377i | \(0.0997859\pi\) | ||||
−0.951264 | + | 0.308377i | \(0.900214\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −41.3827 | − | 17.6769i | −1.59282 | − | 0.680385i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.52628 | − | 5.50000i | −0.366125 | − | 0.211382i | 0.305639 | − | 0.952147i | \(-0.401130\pi\) |
−0.671764 | + | 0.740765i | \(0.734463\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −40.5000 | + | 70.1481i | −1.55196 | + | 2.68808i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −34.6410 | + | 20.0000i | −1.32550 | + | 0.765279i | −0.984600 | − | 0.174820i | \(-0.944066\pi\) |
−0.340901 | + | 0.940099i | \(0.610732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.00000 | + | 8.00000i | −0.152832 | + | 0.305664i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 78.0000i | − | 2.97589i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | − | 5.19615i | −0.114291 | − | 0.197958i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.0000 | − | 34.6410i | 0.760836 | − | 1.31781i | −0.181584 | − | 0.983375i | \(-0.558123\pi\) |
0.942420 | − | 0.334431i | \(-0.108544\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −18.6603 | + | 12.3205i | −0.707824 | + | 0.467344i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.9808 | − | 15.0000i | 0.984092 | − | 0.568166i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 48.0000 | 1.81553 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −25.0000 | −0.944237 | −0.472118 | − | 0.881535i | \(-0.656511\pi\) | ||||
−0.472118 | + | 0.881535i | \(0.656511\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −69.2820 | + | 40.0000i | −2.61302 | + | 1.50863i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −61.5788 | + | 40.6577i | −2.31919 | + | 1.53126i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.50000 | − | 12.9904i | 0.281668 | − | 0.487864i | −0.690127 | − | 0.723688i | \(-0.742446\pi\) |
0.971796 | + | 0.235824i | \(0.0757789\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.0000 | + | 36.3731i | 0.787562 | + | 1.36410i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.00000i | − | 0.149801i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.00000 | + | 6.00000i | −0.112194 | + | 0.224387i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −12.9904 | + | 7.50000i | −0.485135 | + | 0.280093i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.00000 | + | 1.73205i | −0.0372937 | + | 0.0645946i | −0.884070 | − | 0.467355i | \(-0.845207\pi\) |
0.846776 | + | 0.531949i | \(0.178540\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −46.7654 | − | 27.0000i | −1.73922 | − | 1.00414i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.96410 | − | 4.59808i | 0.0729449 | − | 0.170768i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 28.0000i | − | 1.03846i | −0.854634 | − | 0.519231i | \(-0.826218\pi\) | ||
0.854634 | − | 0.519231i | \(-0.173782\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000 | + | 17.3205i | 0.369863 | + | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.5070 | − | 20.5000i | −1.31148 | − | 0.757185i | −0.329141 | − | 0.944281i | \(-0.606759\pi\) |
−0.982342 | + | 0.187096i | \(0.940092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.9808 | + | 15.0000i | 0.957014 | + | 0.552532i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.50000 | − | 4.33013i | −0.0919640 | − | 0.159286i | 0.816373 | − | 0.577524i | \(-0.195981\pi\) |
−0.908337 | + | 0.418238i | \(0.862648\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 24.0000 | 0.881662 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 30.0000i | − | 1.10059i | −0.834969 | − | 0.550297i | \(-0.814515\pi\) | ||
0.834969 | − | 0.550297i | \(-0.185485\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.803848 | − | 13.3923i | −0.0294507 | − | 0.490656i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 62.3538 | + | 36.0000i | 2.28141 | + | 1.31717i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.50000 | + | 11.2583i | −0.237188 | + | 0.410822i | −0.959906 | − | 0.280321i | \(-0.909559\pi\) |
0.722718 | + | 0.691143i | \(0.242893\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.19615 | + | 3.00000i | −0.189358 | + | 0.109326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 18.0000 | + | 9.00000i | 0.655087 | + | 0.327544i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 48.0000i | − | 1.74459i | −0.488980 | − | 0.872295i | \(-0.662631\pi\) | ||
0.488980 | − | 0.872295i | \(-0.337369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | − | 15.5885i | −0.326679 | − | 0.565825i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0000 | + | 32.9090i | −0.688749 | + | 1.19295i | 0.283493 | + | 0.958974i | \(0.408507\pi\) |
−0.972243 | + | 0.233975i | \(0.924827\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 36.9615 | + | 55.9808i | 1.33635 | + | 2.02399i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.66025 | + | 5.00000i | −0.312704 | + | 0.180540i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.0000 | 0.576975 | 0.288487 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288487 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −23.3827 | + | 13.5000i | −0.841017 | + | 0.485561i | −0.857610 | − | 0.514301i | \(-0.828051\pi\) |
0.0165929 | + | 0.999862i | \(0.494718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.92820 | + | 1.19615i | −0.356632 | + | 0.0429671i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 24.0000 | − | 41.5692i | 0.859889 | − | 1.48937i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.00000i | − | 0.321634i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −18.0000 | + | 36.0000i | −0.642448 | + | 1.28490i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.59808 | + | 1.50000i | −0.0926114 | + | 0.0534692i | −0.545590 | − | 0.838052i | \(-0.683695\pi\) |
0.452979 | + | 0.891521i | \(0.350361\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.0000 | − | 62.3538i | 1.28163 | − | 2.21986i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2.41154 | − | 40.1769i | −0.0855286 | − | 1.42493i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 43.0000i | − | 1.52314i | −0.648084 | − | 0.761569i | \(-0.724429\pi\) | ||
0.648084 | − | 0.761569i | \(-0.275571\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 55.0000 | 1.94576 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 24.0000 | + | 41.5692i | 0.847998 | + | 1.46878i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.9808 | + | 15.0000i | 0.916841 | + | 0.529339i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.19615 | − | 3.00000i | −0.182913 | − | 0.105605i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.50000 | − | 9.52628i | −0.193370 | − | 0.334926i | 0.752995 | − | 0.658026i | \(-0.228608\pi\) |
−0.946365 | + | 0.323100i | \(0.895275\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.00000 | −0.210688 | −0.105344 | − | 0.994436i | \(-0.533594\pi\) | ||||
−0.105344 | + | 0.994436i | \(0.533594\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.3923 | + | 0.803848i | −0.469112 | + | 0.0281576i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 27.7128 | + | 16.0000i | 0.969549 | + | 0.559769i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5000 | + | 38.9711i | −0.785255 | + | 1.36010i | 0.143591 | + | 0.989637i | \(0.454135\pi\) |
−0.928846 | + | 0.370465i | \(0.879198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.5885 | − | 9.00000i | 0.543379 | − | 0.313720i | −0.203068 | − | 0.979165i | \(-0.565091\pi\) |
0.746447 | + | 0.665444i | \(0.231758\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −36.0000 | + | 27.0000i | −1.25336 | + | 0.940019i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 22.0000i | − | 0.765015i | −0.923952 | − | 0.382507i | \(-0.875061\pi\) | ||
0.923952 | − | 0.382507i | \(-0.124939\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.0000 | − | 29.4449i | −0.590434 | − | 1.02266i | −0.994174 | − | 0.107788i | \(-0.965623\pi\) |
0.403739 | − | 0.914874i | \(-0.367710\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −21.0000 | + | 36.3731i | −0.728482 | + | 1.26177i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.69615 | + | 5.59808i | 0.127911 | + | 0.193729i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −15.5885 | + | 9.00000i | −0.538816 | + | 0.311086i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.0000 | −1.58810 | −0.794048 | − | 0.607855i | \(-0.792030\pi\) | ||||
−0.794048 | + | 0.607855i | \(0.792030\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 38.9711 | − | 22.5000i | 1.34224 | − | 0.774941i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −22.3923 | + | 14.7846i | −0.770319 | + | 0.508606i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5000 | + | 18.1865i | −0.360359 | + | 0.624160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −10.0000 | − | 17.3205i | −0.342796 | − | 0.593739i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0000i | 0.890223i | 0.895475 | + | 0.445112i | \(0.146836\pi\) | ||||
−0.895475 | + | 0.445112i | \(0.853164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 96.0000 | + | 48.0000i | 3.28313 | + | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0526 | − | 11.0000i | 0.650823 | − | 0.375753i | −0.137948 | − | 0.990439i | \(-0.544051\pi\) |
0.788771 | + | 0.614687i | \(0.210717\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.0000 | + | 20.7846i | −0.409435 | + | 0.709162i | −0.994826 | − | 0.101589i | \(-0.967607\pi\) |
0.585392 | + | 0.810751i | \(0.300941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 39.8372 | + | 23.0000i | 1.35607 | + | 0.782929i | 0.989092 | − | 0.147299i | \(-0.0470581\pi\) |
0.366981 | + | 0.930228i | \(0.380391\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −20.0885 | + | 1.20577i | −0.683028 | + | 0.0409975i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 24.0000i | − | 0.815083i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 21.0000 | 0.712376 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.00000 | − | 8.66025i | −0.169419 | − | 0.293442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.5885 | − | 9.00000i | −0.527589 | − | 0.304604i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.6410 | − | 20.0000i | −1.16974 | − | 0.675352i | −0.216124 | − | 0.976366i | \(-0.569342\pi\) |
−0.953620 | + | 0.301014i | \(0.902675\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 22.5000 | + | 38.9711i | 0.758906 | + | 1.31446i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.0000 | 1.61716 | 0.808581 | − | 0.588386i | \(-0.200236\pi\) | ||||
0.808581 | + | 0.588386i | \(0.200236\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.00000i | − | 0.134611i | −0.997732 | − | 0.0673054i | \(-0.978560\pi\) | ||
0.997732 | − | 0.0673054i | \(-0.0214402\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −66.9615 | + | 4.01924i | −2.25089 | + | 0.135105i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.3923 | + | 6.00000i | 0.348939 | + | 0.201460i | 0.664218 | − | 0.747539i | \(-0.268765\pi\) |
−0.315279 | + | 0.948999i | \(0.602098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | + | 23.3827i | −0.452267 | + | 0.783349i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 76.2102 | − | 44.0000i | 2.55028 | − | 1.47240i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | − | 4.00000i | −0.267411 | − | 0.133705i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.00000i | 0.200334i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.00000 | − | 1.73205i | −0.0333519 | − | 0.0577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.0000 | + | 25.9808i | −0.499722 | + | 0.865545i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.6603 | + | 12.3205i | −0.620288 | + | 0.409548i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.9090 | − | 19.0000i | 1.09272 | − | 0.630885i | 0.158424 | − | 0.987371i | \(-0.449359\pi\) |
0.934300 | + | 0.356487i | \(0.116025\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −72.0000 | −2.38809 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −52.0000 | −1.72284 | −0.861418 | − | 0.507896i | \(-0.830423\pi\) | ||||
−0.861418 | + | 0.507896i | \(0.830423\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31.1769 | − | 18.0000i | 1.03181 | − | 0.595713i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.5000 | + | 47.6314i | −0.907141 | + | 1.57121i | −0.0891245 | + | 0.996020i | \(0.528407\pi\) |
−0.818017 | + | 0.575194i | \(0.804926\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.5000 | + | 49.3634i | 0.939107 | + | 1.62658i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −40.0000 | + | 30.0000i | −1.31519 | + | 0.986394i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 25.9808 | − | 15.0000i | 0.853320 | − | 0.492665i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.00000 | − | 15.5885i | 0.295280 | − | 0.511441i | −0.679770 | − | 0.733426i | \(-0.737920\pi\) |
0.975050 | + | 0.221985i | \(0.0712536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 31.1769 | + | 18.0000i | 1.02069 | + | 0.589294i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 33.4808 | − | 2.00962i | 1.09494 | − | 0.0657216i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 7.00000i | − | 0.228680i | −0.993442 | − | 0.114340i | \(-0.963525\pi\) | ||
0.993442 | − | 0.114340i | \(-0.0364753\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.0000 | 0.685309 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.0000 | − | 34.6410i | −0.651981 | − | 1.12926i | −0.982641 | − | 0.185515i | \(-0.940605\pi\) |
0.330660 | − | 0.943750i | \(-0.392729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.3923 | + | 6.00000i | 0.338420 | + | 0.195387i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.19615 | − | 3.00000i | −0.168852 | − | 0.0974869i | 0.413192 | − | 0.910644i | \(-0.364414\pi\) |
−0.582045 | + | 0.813157i | \(0.697747\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −84.0000 | −2.72389 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 42.0000i | 1.36051i | 0.732974 | + | 0.680257i | \(0.238132\pi\) | ||||
−0.732974 | + | 0.680257i | \(0.761868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.937822 | − | 15.6244i | −0.0303472 | − | 0.505592i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.79423 | − | 4.50000i | −0.251952 | − | 0.145464i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13.5000 | − | 23.3827i | 0.435484 | − | 0.754280i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −41.5692 | + | 24.0000i | −1.33955 | + | 0.773389i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000 | − | 16.0000i | 0.257529 | − | 0.515058i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000i | 0.257263i | 0.991692 | + | 0.128631i | \(0.0410584\pi\) | ||||
−0.991692 | + | 0.128631i | \(0.958942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −60.0000 | − | 103.923i | −1.92748 | − | 3.33849i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.00000 | − | 15.5885i | 0.288824 | − | 0.500257i | −0.684706 | − | 0.728820i | \(-0.740069\pi\) |
0.973529 | + | 0.228562i | \(0.0734025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.8923 | − | 1.79423i | 0.476935 | − | 0.0574613i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.9615 | + | 30.0000i | −1.66240 | + | 0.959785i | −0.690830 | + | 0.723017i | \(0.742755\pi\) |
−0.971566 | + | 0.236768i | \(0.923912\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.0000 | 0.767043 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −42.0000 | −1.34096 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2583 | − | 6.50000i | 0.359085 | − | 0.207318i | −0.309594 | − | 0.950869i | \(-0.600193\pi\) |
0.668679 | + | 0.743551i | \(0.266860\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3205 | − | 18.6603i | −0.392564 | − | 0.594565i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | + | 6.92820i | −0.127193 | + | 0.220304i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 60.0000i | 1.90404i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 36.0000 | + | 18.0000i | 1.14128 | + | 0.570638i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 45.8993 | − | 26.5000i | 1.45365 | − | 0.839263i | 0.454961 | − | 0.890511i | \(-0.349653\pi\) |
0.998686 | + | 0.0512480i | \(0.0163199\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −45.0000 | + | 77.9423i | −1.42374 | + | 2.46598i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))